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Fully extending modulesKeywords: Closed submodules , Quasi closed submodules , Extending modules , Fully extending modules , Strongly extending modules , Modules has SIP property Abstract: Throughout this paper we introduce the concept of quasi closed submoduleswhich is weaker than the concept of closed submodules. Byusing this concept we define the class of fully extending modules, wherean R-module M is called fully extending if every quasi closed submoduleof M is a direct summand.This class of modules is stronger than theclass of extending modules. Many results about this concept are given,also many relationships with other related concepts are introduced.
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